line that is drawenne frome the one to the other, is the line A.B, which as you see, must needes lyghte within the circle. So if you putte the pointes to be A.D, or D.C, or A.C, other B.C, or B.D, in any of these cases you see, that the line that is drawen from the one pricke to the other dothe euermore run within the edge of the circle, els canne it be no right line. How be it, that a croked line, especially being more croked then the portion of the circumference, maye bee drawen from pointe to pointe withoute the circle. But the theoreme speaketh only of right lines, and not of croked lines.
[ The xlviij. Theoreme.]
If a righte line passinge by the centre of a circle, doo crosse an other right line within the same circle, passinge beside the centre, if he deuide the saide line into twoo equal partes, then doo they make all their angles righte. And contrarie waies, if they make all their angles righte, then doth the longer line cutte the shorter in twoo partes.
Example.
The circle is A.B.C.D, the line that passeth by the centre, is A.E.C, the line that goeth beside the centre is D.B. Nowe
saye I, that the line A.E.C, dothe cutte that other line D.B. into twoo iuste partes, and therefore all their four angles ar righte angles. And contrarye wayes, bicause all their angles are righte angles, therfore it muste be true, that the greater cutteth the lesser into two equal partes, accordinge as the Theoreme would.